We aim to squeeze the beam size down as much as possible at
the collision point to increase the chances of a collision.

Even so… protons are very small things.

So even though we squeeze our 100,000 million protons per
bunch down to 64 microns (about
the width of a human hair) at the interaction point. We get only around 20 collisions per crossing
with nominal beam currents.

The bunches cross (every 25 ns.) so often we end up with around 600 million
collisions per second - at the start of a fill with nominal current.

Most protons miss each other and carry on around the ring time after time.
The beams are kept circulating for hours

Collision rate

By definition event rate = luminosity * cross section

The total proton-proton cross section at 7 TeV is approximately 110 mbarns.
This total can be broken down in contributions from:
• inelastic (sin = 60 mbarn)
• single diffractive (ssd = 12 mbarn)
• elastic (sel = 40 mbarn)

The cross section from elastic scattering of the protons and diffractive
events will not be seen by the detectors as it is only the inelastic scatterings
that give rise to particles at sufficient high angles with respect to the beam
axis.

The bunch spacing in the LHC is 25 ns., however, there are bigger gaps (e.g.
to allow dump kickers the time to get up etc.).

A 25 ns. beam gives
us a peak crossing rate of 40 MHz. Because of the gaps we get an average
crossing rate = number of bunches * revolution frequency = 2808 * 11245 = 31.6
MHz. Times 19 events per crossing at nominal luminosity gives us our 600
million inelastic events per second.